## Abstract

We show in details how to determine and identify the algebra g = {A_{i}} of the infinitesimal symmetry operators of the following pseudo-diffusion equation (PSDE) LQ ≡ [∂∂t−14(∂2∂x2−1t2∂2∂p2)]Q(x, p, t) = 0. This equation describes the behavior of the Q functions in the (x, p) phase space as a function of a squeeze parameter y, where t = e^{2y}. We illustrate how G_{i}(λ) ≡ exp[λA_{i}] can be used to obtain interesting solutions. We show that one of the symmetry generators, A_{4}, acts in the (x, p) plane like the Lorentz boost in (x, t) plane. We construct the Anti-de-Sitter algebra so(3, 2) from quadratic products of 4 of the A_{i}, which makes it the invariance algebra of the PSDE. We also discuss the unusual contraction of so(3, 1) to so(1, 1)∌ h^{2}. We show that the spherical Bessel functions I_{0}(z) and K_{0}(z) yield solutions of the PSDE, where z is scaling and “twist” invariant.

Original language | English |
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Pages (from-to) | 334-339 |

Number of pages | 6 |

Journal | Physics of Atomic Nuclei |

Volume | 80 |

Issue number | 2 |

DOIs | |

State | Published - 1 Mar 2017 |

## ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics